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Then suppose:
#<math>\forall j \ne i \in H \quad i \succ_j h \quad \forall h\ne i,j \in H\quad\mbox{(Everyone Loves loves Brad)}</math>
#<math>\{\emptyset\} \succ_i h \quad \forall h\ne i \in H\quad\mbox{(Brad would rather be alone)}</math>
Then <math>T = \{\emptyset\}</math> Q.E.D.
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